Silicon is one of the most widely used materials in modern photonics and is the main building block within the electronic complementary-metal-oxide-semiconductor (CMOS) process. However, silicon is also a centrosymmetric media, in which second order nonlinear susceptibility (χ(2)) is typically inhibited in the electric-dipole approximation. As a result, it can be challenging to induce nonlinear optical processes based on χ(2), such as second harmonic generation (SHG), sum frequency generation, difference frequency generation, and four wave mixing (e.g. linear electro-optic effects), in silicon devices.
The electro-refractive effect (also referred to as plasma-dispersion effect) based on the change in free-carrier concentration may be utilized to initiate certain electro-optic processes in silicon. As the free-carrier concentration changes in a silicon waveguide, the material polarization can also alter, thereby changing the electric permittivity of silicon. However, this electro-refractive effect is usually still weak (e.g., ΔnSi<10−3), compared to nonlinear crystals, such as LiNbO3.
One way to increase the electro-refractive effect in silicon is to integrate p-n junctions into compact resonant micro-ring and Mach-Zehnder modulators. By applying a positive or negative bias to these junctions, the free-carriers can be rapidly injected or depleted to modulate the permittivity of silicon. The modulation of the permittivity can in turn induce a phase change in a resonator cavity and an arm of a Mach-Zehnder interferometer, leading to the amplitude modulation of a continuous wave laser at the output of a resonant and a Mach-Zehnder modulator, respectively. In injection based modulators, bandwidths of these modulators can be limited by the free-carrier lifetime in silicon (e.g., τ˜1 ns or 1/τ˜1 GHz), and the power consumption is typically on the order of a pico-joule-per-bit. The electrical bandwidths of the silicon modulators may be extended by depleting carriers (e.g., f3 dB>20 GHz) and power consumption of the modulation can be reduced down to a single femto-joule-per-bit. However, this improvement usually comes at a price of high free-carrier loss and large capacitance per-unit-volume. This can impose a trade-off between the device bandwidth and power consumption.
Alternatively, nonlinear electro-optic effects based on second and third order susceptibilities can scale with the applied electric field and usually do not impose a trade-off like the electro-refractive effect. In fact, the upper limit of the nonlinear electro-optic effect is imposed only by the silicon breakdown field which is Eb˜6×107V/m.
One approach for generating the electro-optic effect in silicon includes depositing a SiN stressor layer on a silicon waveguide to induce large stress gradients. Silicon waveguides formed using this method can have Pockel's like modulation up to about 500 KHz with an applied voltage of 30 Vpp for a <122 pm/V and second harmonic generation (P2ω/Pω=−73 dB) for a χ(2)˜44 pm/V. However, introduction of stressor SiN layer can add process complexity and limit the electro-optic design.
Another approach for generating electro-optic effect in silicon is converting the third order non-linear susceptibility χ(3) to second order non-linear susceptibility χ(2) by the external static or low frequency electric field. An external electric field can be applied to orient dipole moments in the direction of this field, breaking the crystalline symmetry. This effect, also referred as the “electro-optic DC Kerr effect” or “quadratic field effect”, can be conveniently generated in silicon, because silicon exhibits a large χ(3) compared to other CMOS compatible materials, such as SiN and SiO2. In addition, ion implantation can be used to form junctions in silicon, allowing concentration of large electrical fields within silicon and elimination of external electrodes. The field induced χ(2) can be observed in the form of second harmonic generation (SHG). However, SHG efficiency can be relatively low due to the lack of phase matching in silicon waveguides and losses at the operating wavelength.